scholarly journals Consensus of Multi-Integral Fractional-Order Multiagent Systems with Nonuniform Time-Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Jun Liu ◽  
Wei Chen ◽  
Kaiyu Qin ◽  
Ping Li
Keyword(s):  
Numerical Simulations ◽  
Frequency Domain ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Multiple Integral ◽  
Frequency Domain Method ◽  
Double Integral ◽  
Single Integral ◽  
Special Case

Consensus of fractional-order multiagent systems (FOMASs) with single integral has been wildly studied. However, the dynamics with multiple integral (especially double integral to sextuple integral) also exist in FOMASs, and they are rarely studied at present. In this paper, consensus problems for multi-integral fractional-order multiagent systems (MIFOMASs) with nonuniform time-delays are addressed. The consensus conditions for MIFOMASs are obtained by a novel frequency-domain method which properly eliminates consensus problems of the systems associated with nonuniform time-delays. Besides, the method revealed in this paper is applicable to classical high-order multiagent systems which is a special case of MIFOMASs. Finally, several numerical simulations with different parameters are performed to validate the correctness of the results.

scholarly journals Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li ◽  
Mengji Shi
Keyword(s):  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
External Environment ◽  
Domain Theory ◽  
Dynamical Model ◽  
Integer Order ◽  
The Laplace Transform ◽  
Simulation Results ◽  
Theoretical Results

Due to the complex external environment, many multiagent systems cannot be precisely described or even cannot be described by an integer-order dynamical model and can only be described by a fractional-order dynamical model. In this paper, consensus problems are investigated for two types of fractional-order multiagent systems (FOMASs) with nonuniform time delays: FOMAS with symmetric time delays and undirected topology and FOMAS with asymmetric time delays and directed topology. Employing the Laplace transform and the frequency-domain theory, two delay margins are obtained to guarantee the consensus for the two types of FOMAS, respectively. These results are also suitable for the integer-order dynamical model. Finally, simulation results are provided to illustrate the effectiveness of our theoretical results.

scholarly journals Consensus of Delayed Fractional-Order Multiagent Systems Based on State-Derivative Feedback

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Liu ◽  
Kaiyu Qin ◽  
Wei Chen ◽  
Ping Li
Keyword(s):  
Graph Theory ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Multiagent System ◽  
Frequency Domain Analysis ◽  
Consensus Control ◽  
Control Protocol ◽  
Analysis Theory ◽  
Theoretical Results

A state-derivative feedback (SDF) is added into the designed control protocol in the existing paper to enhance the robustness of a fractional-order multiagent system (FMS) against nonuniform time delays in this paper. By applying the graph theory and the frequency-domain analysis theory, consensus conditions are derived to make the delayed FMS based on state-derivative feedback reach consensus. Compared with the consensus control protocol designed in the existing paper, the proposed SDF control protocol with nonuniform time delays can make the FMS with SDF and nonuniform time delays tolerate longer time delays, which means that the convergence speed of states of the delayed FMS with SDF is accelerated indirectly. Finally, the corresponding results of simulation are given to verify the feasibility of our theoretical results.

scholarly journals Consensus Analysis for a Class of Heterogeneous Multiagent Systems with Time Delay Based on Frequency Domain Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yi-Jie Sun ◽  
Guo-liang Zhang ◽  
Jing Zeng
Keyword(s):  
Time Delay ◽  
Frequency Domain ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Frequency Domain Method ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Domain Method ◽  
Communication Topology ◽  
System Coupling

The consensus problem of heterogeneous multiagent systems composed of first-order and second-order agent is investigated. A linear consensus protocol is proposed. Based on frequency domain method, the sufficient conditions of achieving consensus are obtained. If communication topology contains spanning tree and some conditions can be satisfied on control gains, consensus can be achieved. Then, a linear consensus protocol with time delay is proposed. In this case, consensus is dependent only on system coupling strength, each agent input time delay, but independent of communication delay. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical result.

scholarly journals Consensus Conditions for a Class of Fractional-Order Nonlinear Multiagent Systems with Constant and Time-Varying Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaorong Zhang ◽  
Min Shi
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Time Delays ◽  
Constant Time Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay ◽  
Theoretical Results

The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.

scholarly journals An Improved Frequency-domain Method for the Fractional Order PI λ D µ Controller Optimal Design

2018 ◽  
Vol 51 (4) ◽  
pp. 681-686
Author(s):  
Weijia Zheng ◽  
Ying Luo ◽  
Yangquan Chen ◽  
Youguo Pi ◽  
Wei Yu
Keyword(s):  
Optimal Design ◽  
Frequency Domain ◽  
Fractional Order ◽  
Frequency Domain Method ◽  
Domain Method

scholarly journals A Fractional-Order Model for Zika Virus Infection with Multiple Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
R. Rakkiyappan ◽  
V. Preethi Latha ◽  
Fathalla A. Rihan
Keyword(s):  
Hopf Bifurcation ◽  
Virus Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Zika Virus ◽  
Epidemic Model ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Zika Virus Infection

Time delays and fractional order play a vital role in biological systems with memory. In this paper, we propose an epidemic model for Zika virus infection using delay differential equations with fractional order. Multiple time delays are incorporated in the model to consider the latency of the infection in a vector and the latency of the infection in the infected host. We investigate the necessary and sufficient conditions for stability of the steady states and Hopf bifurcation with respect to three time delays τ1, τ2, and τ3. The model undergoes a Hopf bifurcation at the threshold parameters τ1∗, τ2∗, and τ3∗. Some numerical simulations are given to show the effectiveness of obtained results. The numerical simulations confirm that combination of fractional order and time delays in the epidemic model effectively enriches the dynamics and strengthens the stability condition of the model.

Regularity and stability of coupled plate equations with indirect structural or Kelvin-Voigt damping

2019 ◽  
Vol 25 ◽  
pp. 51 ◽  
Author(s):  
Zhong-Jie Han ◽  
Zhuangyi Liu
Keyword(s):  
Spectral Analysis ◽  
Exponential Stability ◽  
Numerical Simulations ◽  
Frequency Domain ◽  
Frequency Domain Method ◽  
Structural Damping ◽  
One Dimensional ◽  
Domain Method ◽  
Plate Equations ◽  
Exponentially Stable

In this paper, the regularity and stability of the semigroup associated with a system of coupled plate equations is considered. Indirect structural or Kelvin-Voigt damping is imposed, i.e., only one equation is directly damped by one of these two damping. By the frequency domain method, we show that the associated semigroup of the system with indirect structural damping is analytic and exponentially stable. However, with the much stronger indirect Kelvin-Voigt damping, we prove that, by the asymptotic spectral analysis, the semigroup is even not differentiable. The exponential stability is still maintained. Finally, some numerical simulations of eigenvalues of the corresponding one-dimensional systems are also given.

scholarly journals Networked Convergence of Fractional-Order Multiagent Systems with a Leader and Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Yuntao Shi ◽  
Junjun Zhang
Keyword(s):  
Numerical Simulations ◽  
Multiagent Systems ◽  
Fractional Order ◽  
Discrete Time ◽  
Sampling Interval

This paper investigates the convergence of fractional-order discrete-time multiagent systems with a leader and sampling delay by using Hermite-Biehler theorem and the change of bilinearity. It is shown that such system can achieve convergence depending on the sampling intervalh, the fractional-orderα, and the sampling delayτand its interconnection topology. Finally, some numerical simulations are given to illustrate the results.

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